ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
243 
The general problem of illumination is how to causo the luminous 
rays emitted by a source of light to converge upon the object under a 
certain angle ; but since in every optical apparatus the path of the 
luminous rays can be considered as reciprocal, it is more convenient 
to transform this and consider that the problem to bo solved is to find 
the conditions in which all the rays of a pencil emanating from the 
object under a given angle shall meet a source of light. 
As regards the achromatism of the illumination, if all the coloured 
rays emanating from a point of the object meet the source of light, the 
illumination of that part will be achromatic ; but if this is not the case, 
it will be coloured by a colour complementary to that of the rays which 
do not meet the source of light. 
Two cases of illumination are considered. 
(1) The luminous source has dimensions relatively indefinite. Sup- 
pose that the rays of the pencil from the object have an angular aperture 
sufficiently small not to extend beyond the limits of the mirror MM' 
and that their prolongations SS' passing freely across the window FF 1 
lose themselves in a clear blue sky (fig. 22). In this case it is evident 
Fig. 22. 
that if the rays 0 M and 0 M' always start from the object in the same 
directions, whatever modifications these directions may afterwards under- 
go, the effect produced will be the same. Thus, as seen in fig. 23, the 
interposition of the lens LL' and the curved mirror MM' in place of 
